A triangle center is a point whose Trilinear Coordinates are defined in terms of the side lengths and angles of a Triangle. The function giving the coordinates is called the Triangle Center Function. The four ancient centers are the Centroid, Incenter, Circumcenter, and Orthocenter. For a listing of these and other triangle centers, see Kimberling (1994).

A triangle center is said to be Regular Iff there is a Triangle Center
Function which is a Polynomial in , , , and (where is the Area of the
Triangle) such that the Trilinear Coordinates of the center are

A triangle center is said to be a Major Triangle Center if the Triangle Center Function is a function of Angle alone, and therefore and of and alone, respectively.

**References**

Davis, P. J. ``The Rise, Fall, and Possible Transfiguration of Triangle Geometry: A Mini-History.''
*Amer. Math. Monthly* **102**, 204-214, 1995.

Dixon, R. ``The Eight Centres of a Triangle.'' §1.5 in *Mathographics.* New York: Dover, pp. 55-61, 1991.

Gale, D. ``From Euclid to Descartes to Mathematica to Oblivion?'' *Math. Intell.* **14**, 68-69, 1992.

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' *Math. Mag.* **67**, 163-167, 1994.

Kimberling, C. ``Triangle Centers and Central Triangles.'' *Congr. Numer.* **129**, 1-295, 1998.

© 1996-9

1999-05-26